self Maths Puzzle

The school children were returning to their homes when they met the mathematical milkman, who propounds the following problem:

In one of the two cans there is milk which is so rich with cream that it becomes absolutely necessary to dilute it with a little water to make it wholesome.

Therefore, in the other can there is some pure spring water, now I proceed to pour spring water from can No. 1 into can No. 2 sufficient to double its contents, and then repour from No. 2 into No.1 enough of the mixture to double the contents.

Then to equalize matters, I again pour from No. 1 into No. 2 to double the contents of No. 2 and find the same number of gallons of milk in each can, although there is one more gallon of water in can No. 2 than there is milk, so I want you to tell me how much more water than milk is there in can No. 1?

Read Solution (Total 1)

Suppose, in the beginning there was x gallons of spring water in can No 1 and y gallons of milk in can No. 2 then,

can No. 1 | can No. 2
|
In the Beginning x gallons of water | y gallons of milk
|
After doubling contents of Can 2 x-y | 2y
water = x-y, | water=y,
milk = 0 | milk=y
|
|
After doubling contents of Can 1 2(x-y) | 2y-(x-y)i.e (3y-x)
water = 2(3/4)(x-y), | water=(1/2)(3y-x),
milk = 2(1/4)(x-y) | milk=(1/2)(3y-x)
|
After doubling contents of Can 2 |
2(x-y)-(3y-x) ie (3x-5y) | 2(3y-x)
water = (3/4)(3x-5y), | water = (5/4)(3y-x),
milk = (1/4)(3x-5y) | milk = (3/4)(3y-x)

Now, we know that the number of gallons of Milk in Can 1 = number of gallons of Milk in Can 2

Hence: (1/4)(3x-5y) = (3/4)(3y-x)
Multiply by 4: 3x-5y = 3(3y-x)
Move x to one side and y to other: 6x = 14y
And so: x = (14/6)y

We ALSO know that the number of gallons of Water in Can 2 = number of gallons of Milk in Can 2 PLUS 1

Hence (5/4)(3y-x) = (3/4)(3y-x) +1
Multiply by 4: 5(3y-x) = 3(3y-x) + 4
Simplify: 2(3y-x) = 4
Replace "x" with "(14/6)y": 2(3y-(14/6)y) = 4
Simplify: (4/3)y = 4
Hence: y = 3

Now we know y=3, we also know that x = (14/6)y = 7

Hence, there was initially 7 gallons of water in can No. 1 and 3 gallons of milk in can No 2.

After all the mixings there would be 4½ gallons of water and 1½ gallons of milk in can No. 1 and 2 1/2gallons of water and 1 1/2 gallons of milk in can No 2.

Hence, there is 3 more gallons of water than milk in can No 1.
12 years agoHelpfull: Yes(1) No(0)

self Other Question

An Arab Sheik, finding himself about to die, called his sons about him and said: "Divide my camels among you in the proportion of one-half of the herd to the eldest son, the second son one-third, and to the youngest son one-ninth."
Thereupon the oldest son cried: "O, my father, one-half, one-third, and one-ninth do not constitute a whole. To whom, therefore, shall the remainder of the herd be given?"

"To any poor man who may be standing by when the division is made," replied the Sheik, who thereupon died.

When the herd was collected a new difficulty arose. The number of the camels could not be divided either by two or three or nine. While the brothers were disputing, a poor but crafty Bedouin, standing by with his camel, exclaimed, "Behold, I will sell you my beast for ten pieces of silver, so that you may then divide the herd."

Seeing that the addition of one camel would solve the difficulty, the brothers jumped at the offer, and proceeded to divide the herd, but when each had received his allotted portion there yet remained one camel.

"I am the poor man standing by." Said the crafty Bedouin, and gaily mounting the camel, he rode away, with the ten pieces of silver in his turban.

Now, how many camels were in the Sheik's herd? This odd little problem in domestic arithmetic was sprung by the cook upon Mrs. Smith when she wanted to know what the grocer charged for such small eggs.

"I paid twelve cents for the lot," replied Bridget, "but I made him throw in two extra ones, because they were so little, and you see that made them cost one cent a dozen less than his first asking price!"

Tell now how many eggs she received for her twelve cents?